
where \(C_{1}\)  – \(C_{4}\)  are constant coefficients, \(J_{\nu }\)  and \(Y_{\nu }\)  are
the Bessel and Neumann functions of corresponding orders, respectively.
Using standard methods from the theory of scattering [1]}, [2]},
we obtain the expressions for the partial elements of the \(S\) -matrix in terms
of the coefficients \(C_{1}\)  – \(C_{4}\)
\(S_{1/2,1/2}^{\left( +1\right) } &=&\frac{C_{1}-iC_{2}}{C_{1}+iC_{2}}, \\S_{-1/2,1/2}^{\left( +1\right) } &=&\frac{2p}{\varepsilon -h}\frac{C_{3}}{C_{1}+iC_{2}}.\) 
